Preheat your oven to 300° Fahrenheit.
Pat the short ribs dry with paper towels, and season them generously with kosher salt and black pepper.
Let them rest on a baking rack for 30 minutes.
Heat olive oil in a large Dutch oven over medium-high heat.
Lightly dust both sides of the ribs with all-purpose flour. Once the oil is hot, add the beef short ribs and sear them for a few minutes on each side.
Remove the ribs from the pot and set aside.
Add the onions, celery, and carrots to the pot with a pinch of salt and pepper. Sauté until tender, about 10 minutes.
Add minced garlic, beef base, and tomato paste to the pot. Stir well and sauté for an additional 1-2 minutes.
Pour in the red wine vinegar, deglazing by scraping the browned bits from the pot bottom.
Pour in the beef broth and return the short ribs to the pot, adding rosemary, thyme, and bay leaves.
Bring the liquid to a low simmer. Cover the pot and transfer it to the oven.